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Svetllana [295]
3 years ago
10

Find the distance from the point A(-2,3) to the line y=1/2x+1. Round your answer to the nearest tenth.

Mathematics
1 answer:
telo118 [61]3 years ago
7 0

Answer:

<h2>2√5</h2>

Step-by-step explanation:

\text{Let}\\\\Ax+By=C-\text{a line}\\\\(x_0,\ y_0)-\text{a point}\\\\\text{The formula of a distance between a point and a line}:\\\\d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}

\text{We have}\\\\y=\dfrac{1}{2}x+1,\ A(-2,\ 3)\\\\\text{Convert the equation of a line to the standard form}:\\\\y=\dfrac{1}{2}x+1\qquad\text{multiply both sides by 2}\\\\2y=x+2\qquad\text{subtract}\ x\ \text{from both sides}\\\\-x+2y=2\qquad\text{change the signs}\\\\x-2y=-2\\\\\text{Substitute}\ A=1,\ B=-2,\ C=-2,\ x_0=-2,\ y_0=3,\ \text{to the formula:}\\\\d=\dfrac{|(1)(-2)+(-2)(3)+(-2)|}{\sqrt{1^2+(-2)^2}}=\dfrac{|-2-6-2|}{\sqrt{1+4}}=\dfrac{|-10|}{\sqrt5}

=\dfrac{10}{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{10\sqrt5}{5}=2\sqrt5

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Step-by-step explanation:

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That is 4/50=1/25

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Answer:

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Step-by-step explanation:

Given data:

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Let the price of the burger be X

Let the price of the medium fries be Y

<em>Equation for the total sale will be </em>3X + 3Y = 17.55 <em>(equation 1)</em>

<em>from this statement 'The price of a burger is .75 more than two times the price of medium fries.' </em>

X - 2Y = 0.75 <em>(equation 2)</em>

<em>There are now two equations and two unknowns, a simultaneous equation is solved to find the cost of the  burger.</em>

<em>Many methods can be used to solve these equations but in this case substitution will be used</em>

<em>From equation 2 </em>

X = 0.75 + 2Y<em> (equation 3)</em>

<em>Substituting equation 3 into equation 1</em>

3(0.75 + 2Y) + 3Y = 17.55

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6Y + 3Y = 17.55-2.25

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6 0
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Klio2033 [76]

Part 1

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Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.

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<h3>Answer: 66</h3>

========================================================

Part 2

Inscribed angle CBA was found to be 66 degrees back in part 1.

This doubles to 132 degrees to represent minor arc AC.

Or you could note that:

minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132

Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.

-----------

Here's what we know about the arc measures of the circle

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  • minor arc BD = 96 degrees

These three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.

Adding those 3 pieces gets us 132+48+96 = 276

This means minor arc AD has to be 360 - 276 = 84 degrees

Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD

84/2 = 42

<h3>Answer:  42</h3>

6 0
1 year ago
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